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group shifts and Bernoulli factors

Published online by Cambridge University Press:  01 April 2008

MIKE BOYLE  and
MICHAEL SCHRAUDNER
MIKE BOYLE
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742-4015, USA (email: mmb@math.umd.edu) Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago de Chile, Chile (email: mschraudner@dim.uchile.cl)
MICHAEL SCHRAUDNER
Affiliation:
Centro de Modelamiento Matemático, Universidad de Chile, Av. Blanco Encalada 2120, Piso 7, Santiago de Chile, Chile (email: mschraudner@dim.uchile.cl)
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Abstract

In this paper, a group shift is an expansive action of on a compact metrizable zero-dimensional group by continuous automorphisms. All group shifts factor topologically onto equal-entropy Bernoulli shifts; abelian group shifts factor by continuous group homomorphisms onto canonical equal-entropy Bernoulli group shifts; and completely positive entropy abelian group shifts are weakly algebraically equivalent to these Bernoulli factors. A completely positive entropy group (even vector) shift need not be topologically conjugate to a Bernoulli shift, and the Pinsker factor of a vector shift need not split topologically.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 28 , Issue 2: William Parry Memorial Volume , April 2008 , pp. 367 - 387
Copyright
Copyright © Cambridge University Press 2008

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